Velocity Constraints Research Articles

Obstacle Avoidance of Surface Agent Formation Based on Streamline Traction at Fixed-Time

The marine environment is highly complex and variable, featuring obstacles such as islands, buoys, and vessels. Safe navigation of the surface agent (SA) fleet is crucial for ensuring the safety of the SA fleet, enhancing operational efficiency, and guaranteeing the smooth execution of the fleet’s mission. Regarding the problem of formation obstacle avoidance for SA fleets encountering complex obstacles during navigation, this chapter presents a fixed-time-based safe navigation algorithm for the SA fleet based on streamline traction. Firstly, to precisely position each SA at the designated location within the formation, a highly malleable leader–follower formation mode is introduced. Based on an enhanced interfered fluid dynamical system (EIFDS) obstacle avoidance algorithm, the virtual Leader is guided to evade static obstacles and determine a trajectory of the designated position. Secondly, a first-order fixed-time control Lyapunov function (FTCLF) is designed based on the EIFDS obstacle avoidance algorithm to guide the angular velocity constraint. The optimal guiding angular velocity signal is obtained through quadratic programming, ensuring that the SA steers towards the designated position while avoiding obstacles. Next, for the guiding velocity amplitude signal, a first-order fixed-time control barrier function (FTCBF) is designed based on the streamline formation scheme and the inter-boat safety distance to guide the velocity amplitude constraint. The optimal guiding velocity amplitude signal is obtained through quadratic programming, guaranteeing that each SA maintains the formation while avoiding collisions with adjacent vessels. Finally, the simulation results indicate the effectiveness, superiority, and stability of the proposed fixed-time-based safe navigation guidance algorithm for the SA fleet based on streamline traction.

Data-Driven Tracking Control of a Cushion Robot with Safe Autonomous Motion Considering Human-Machine Interaction Environment

Abstract This study proposes a data-driven safety controller with velocity constraints for a cushion robot. We constructed a mathematical description of the human-machine interaction environment by decomposing the generalized input force and coefficient matrix in the dynamic model. We established a new equivalent data model, which considered various human-machine interaction environments using a pseudo-Jacobian matrix. A stochastic configuration network (SCN) estimation method for variations in the human-machine interaction environment was proposed, with hidden layer nodes added at random. We designed a safe autonomous navigation path and proposed a data-driven control method that limited the actual velocity while stabilizing the tracking error system. In addition, the desired motion velocity of the robot was designed. This approach has the advantage of ensuring safety at a specified velocity. We also demonstrated and validated the effectiveness of the proposed data-driven algorithm using simulation-based comparative analysis and an experimental study.

Refined Metamodel Disturbance Observer-Based Control for Coarse Pointing Assembly Under Constraints

The target tracking performance of the coarse pointing assembly (CPA) is a critical factor in determining the data transmission efficiency of the inter-satellite laser communication. However, under the influence of multiple disturbances, such as gimbal coupling torque, friction, and satellite-transmitted vibration, the angle tracking performance of the CPA can be decreased, which then affects the safety of the system in terms of angular velocity. To address the performance and safety requirements of the CPA, this paper proposes a refined metamodel disturbance observer-based state constraints controller. First, a refined metamodel disturbance observer is proposed to achieve accurate disturbance estimation by combining the data-driven state-space Kriging metamodeling method with a refined disturbance observer. Both disturbance numerical data and partially known information (e.g. vibration frequency and structure) are fully utilized to reduce estimation conservatism. Second, based on the observer, a state constraint controller is designed to ensure the angle tracking performance and angular velocity constraints. Finally, the effectiveness and robustness of the proposed control method are validated through numerical simulations, indicating an enhanced angle tracking performance compared to the traditional disturbance observer-based control method.

A Triangular Structure Constraint for Pedestrian Positioning with Inertial Sensors Mounted on Foot and Shank

To suppress pedestrian positioning drift, a velocity constraint commonly known as zero-velocity update (ZUPT) is widely used. However, it cannot correct the error in the non-zero velocity interval (non-ZVI) or observe heading errors. In addition, the positioning accuracy will be further affected when a velocity error occurs in the ZVI (e.g., foot tremble). In this study, the foot, ankle, and shank were regarded as a triangular structure. Consequently, an angle constraint was established by utilizing the sum of the internal angles. Moreover, in contrast to the traditional ZUPT algorithm, a velocity constraint method combined with Coriolis theorem was constructed. Magnetometer measurements were used to correct heading. Three groups of experiments with different trajectories were carried out. The ZUPT method of the single inertial measurement unit (IMU) and the distance constraint method of dual IMUs were employed for comparisons. The experimental results showed that the proposed method had high accuracy in positioning. Furthermore, the constraints built by the lower limb structure were applied to the whole gait cycle (ZVI and non-ZVI).

Neurodynamics-based formation tracking control of leader-follower nonholonomic multiagent systems

This paper uses a bioinspired neurodynamic (BIN) approach to investigate the formation control problem of leader-follower nonholonomic multiagent systems. In scenarios where not all followers can receive the leader's state, a distributed adaptive estimator is presented to estimate the leader's state. The distributed formation controller, designed using the backstepping technique, utilizes the estimated leader states and neighboring formation tracking error. To address the issue of impractical velocity jumps, a BIN-based approach is integrated into the backstepping controller. Furthermore, considering the practical applications of nonholonomic multiagent systems, a backstepping controller with a saturation velocity constraint is proposed. Rigorous proofs are provided. Finally, the effectiveness of the presented formation control law is illustrated through numerical simulations.

A novel memetic algorithm for distributed shape formation of swarm robots with both acceleration and velocity constraints

A novel memetic algorithm for distributed shape formation of swarm robots with both acceleration and velocity constraints

A Matrix-Based Approach to Unified Synthesis of Planar Four-Bar Mechanisms for Motion Generation With Position, Velocity, and Acceleration Constraints

Abstract This paper introduces a novel matrix-based approach for the simultaneous type and dimensional synthesis of planar four-bar linkage mechanisms, accommodating various practical constraints, including position, velocity, acceleration, and joint placements. Traditional design processes segregate type synthesis, the determination of joint and link configurations, from dimensional synthesis, which involves specifying link sizes and pivot locations. This segregation often leads to complexities in addressing the complete design challenge. The novel methodology proposed in this paper departs from the conventional sequential design approach by concurrently evaluating type and dimensional parameters using a data-driven matrix formulation. The crux of the paper’s methodology involves formulating a singular design equation through a transformation matrix, parameterized by the Cartesian parameters of the mechanism’s dyads. This formulation linearly expresses a broad range of constraints, facilitating the identification of viable solutions through singular value decomposition and null space analysis. This integrated approach not only simplifies the synthesis process but also provides direct insights into the mechanism’s parameters, encompassing both type and dimensions, thereby obviating the need for further interpretative steps common to the use of quaternions and kinematic mapping. In essence, the paper presents two main contributions: the development of a unified design equation capable of encompassing a wide array of constraints within the mechanism synthesis process, and the introduction of an algorithm that effectively identifies all potential planar four-bar linkage mechanisms by accurately satisfying up to five constraints. This approach promises to enhance the design and optimization of mechanical systems by offering a more holistic and efficient pathway to mechanism synthesis.

An actuator space optimal kinematic path tracking framework for tendon-driven continuum robots: Theory, algorithm and validation

Path tracking of continuum robots is a fundamental and crucial problem across various applications. In this article, we address this problem by focussing on three aspects. Firstly, we propose an efficient multi-solution inverse kinematics solver for three-section constant curvature robots by bridging the theoretical reduction and the numerical correction. Secondly, we derive a linear tendon-driven actuation model, establishing the connection between the robot configuration space and the actuator space. With this model, we achieve optimal distance planning and optimal time allocation considering the constraints of actuator velocity and acceleration, generating a continuous trajectory directly in the actuator space. Finally, we present our kinematic path tracking framework, which includes offline optimal trajectory planning and online feedforward and feedback control. Experiments are conducted both in simulations and in the real world on our three-section tendon-driven continuum robot. The experiments validate the increased efficiency, higher success rates, and accessibility of multiple solutions offered by our inverse kinematics solver, as well as the optimality in distance planning and time allocation in the actuator space. Performance improvements in tracking accuracy are demonstrated through comparative experiments and the application of our framework in path tracking tasks with obstacles is presented through a case study.

Multi-objective optimal trajectory planning for manipulators based on CMOSPBO

Feasible, smooth, and time-jerk optimal trajectory is essential for manipulators utilized in manufacturing process. A novel technique to generate trajectories in the joint space for robotic manipulators based on quintic B-spline and constrained multi-objective student psychology based optimization (CMOSPBO) is proposed in this paper. In order to obtain the optimal trajectories, two objective functions including the total travelling time and the integral of the squared jerk along the whole trajectories are considered. The whole trajectories are interpolated by quintic B-spline and then optimized by CMOSPBO, while taking into account kinematic constraints of velocity, acceleration, and jerk. CMOSPBO mainly includes improved student psychology based optimization, archive management, and an adaptive ε-constraint handling method. Lévy flights and differential mutation are adopted to enhance the global exploration capacity of the improved SPBO. The ε value is varied with iterations and feasible solutions to prevent the premature convergence of CMOSPBO. Solution density estimation corresponding to the solution distribution in decision space and objective space is proposed to increase the diversity of solutions. The experimental results show that CMOSPBO outperforms than SQP, and NSGA-II in terms of the motion efficiency and jerk. The comparison results demonstrate the effectiveness of the proposed method to generate time-jerk optimal and jerk-continuous trajectories for manipulators.

Robust Neural Visual Inertial Odometry With Deep Velocity Constraint

Robust Neural Visual Inertial Odometry With Deep Velocity Constraint

Time Parametrized Motion Planning

Time can be treated as a free parameter to isotropically stretch the tangent space. A trajectory, which matches the boundary conditions on its configuration, is adjusted so that velocity conditions are met. The modified trajectory is found by substitution, without the computational cost of re-integrating the velocity function. This concept is extended to stretch the tangent space anisotropically. This method of time parametrization especially applies to Geometric Control, where the Pontryagin Maximum Principle minimizes some cost function and matches the boundary configuration constraints but not the velocity constraints. The optimal trajectory is modified by the parametrization so that the cost function is minimized if the stretching is stopped at any time. This is a theoretical contribution, using a wheeled robot example to illustrate the modification of an optimal velocity under multiple parametrizations.

A 3D multiobjective multi-item eco-routing problem for refrigerated fresh products delivery using NSGA-II with hybrid chromosome

In a developing countries, say India, about 40 percent fresh foods are wasted during transportation and $14 billion of post harvest products are lost due to inefficiency of cold supply chain such as using non-refrigerated vehicle during last mile transport. Hence, temperature control through refrigerated transportation is very essential. But, the by-product of this process i.e., carbon emission (CE) due to transportation and refrigeration is detrimental for the world. Only logistic transportation contributes about 25 percent of global CE. Due to the world wide infrastructural development, there are several available routes for the road transportation among different cities. For the maintenance of these routes, there are some toll plazas for collection of money. Some routes also cross the rail lines. For maximum profit, a supplier distributes the products at the earliest as the retailers fix the product’s price with respect to its freshness. Again, this process generates more CE. With these realities, a 3D multiobjective multi-item eco-routing problems for refrigerated fresh products (3DMOMIERPsfRFPs) are developed, where a refrigerated vehicle starts from a depot (refrigerated) and comes back after distributing the fresh products to retailers as per their demands. The optimal routing plan, vehicle’s velocity and preservation rate are determined so that total profit and CE are respectively maximized and minimized simultaneously. For solution, an NSGA-II with different modified operators (NSGA-IIwDOs) is developed with hybrid chromosomes having discrete and continuous variables together, probabilistic selection, problem-specific crossover and generation-dependent mutation. Some performance metrics are presented through NSGA-IIwDOs on the standard TSPLIB problems. Results of 3DMOMIERPsfRFPs without and with specific delivery time slots, road-dependent vehicle velocity and time constraints are evaluated. Pareto front for multiobjective are depicted. As a particular case, results of a previous investigation are obtained. Some of the managerial decisions are observed.

Real-sea validation of a model predictive controller's inherent robustness for medium-scale unmanned trimaran heading

The development of medium-to large-scale and high-performance unmanned surface vehicles (USVs) is a burgeoning trend in intelligent marine systems. The heading controller is crucial for USVs to execute diverse missions, especially given their inherent underactuation characteristics and constraints. Recent efforts have focused on enhancing the robustness of controllers against external disturbances and employed two main strategies: one converges the control error to a bounded residual set through robust modifications, while the other eliminates the error by modelling disturbances. Notably, these enhancements have primarily catered to small USVs, where disturbances significantly impact their manoeuvrability, necessitating such robust control strategies. This focus has somewhat overshadowed the inherent robustness of closed-loop control systems. Compared with small USVs, medium-to large-scale USVs are less affected by external disturbances, despite undertaking more complex missions. Leveraging the intrinsic robustness of controllers presents an opportunity to simplify controller design, thereby reallocating computational resources towards enhancing mission capabilities. Model Predictive Control (MPC) has attracted significant attention recently, and its receding horizon and optimality theoretically provides a new level of inherent robustness, which remains under-explored in real sea. This paper focuses on the inherent robustness of MPC in managing the heading of a medium-scale unmanned trimaran subjected to the thrust angle and angular velocity constraints. A model predictive controller considering the constraints is designed based on the identified Nomoto model and the asymptotic stability is ensured with a terminal cost. Conducted real-sea experiments and comparative analyses with a Proportional-Integral-Derivative (PID) controller, the most widespread and dominant control algorithm in practical USV engineering, underscore the superiority of MPC in maintaining satisfactory closed-loop performance. Furthermore, the MPC controller is also successfully applied to real-sea path-following missions and demonstrated good tracking performance in various sea conditions ranging from level 3 to 5 and wind speeds spanning from level 6 to 8. This validation opens up new avenues for motion control strategies in the evolving landscape of larger-scale USVs.

Adaptive Saturated Obstacle Avoidance Trajectory Tracking Control for Euler–Lagrange Systems With Velocity Constraints

ABSTRACTThis article pays attention to the obstacle avoidance trajectory tracking control problem for uncertain Euler–Lagrange (EL) systems subject to velocity constraints and input saturation. The existing obstacle avoidance results do not consider velocity constraints under input saturation, which means that an EL system may not be able to obtain sufficient control inputs to avoid a collision with an obstacle if it has a high speed when approaching the obstacle. Therefore, the velocity constraints in the obstacle avoidance tracking control are considered in this paper. A novel velocity constraint function that depends on the distance between the system and the obstacle is proposed. Integral‐multiplicative Lyapunov‐barrier functions (LBFs) are constructed and incorporated into the backstepping procedure to design an adaptive fuzzy obstacle avoidance tracking control scheme. Moreover, an auxiliary dynamic system is designed by constructing a bounded nonlinear vector related to an auxiliary variable to compensate for the effects of saturation. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the protocol achieves obstacle avoidance for the EL system without violating the velocity constraints inside the obstacle detection region, while also guaranteeing the ultimate uniform boundedness of all the closed‐loop signals. Numerical simulations are presented to demonstrate the efficacy of the proposed control strategy.

Continuous planning for inertial-aided systems

Inertial-aided systems require continuous motion excitation among other reasons to characterize the measurement biases that will enable accurate integration required for localization frameworks. This paper proposes the use of informative path planning to find the best trajectory for minimizing the uncertainty of IMU biases and an adaptive traces method to guide the planner towards trajectories that aid convergence. The key contribution is a novel regression method based on Gaussian Process (GP) to enforce continuity and differentiability between waypoints from a variant of the RRT∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {RRT}^*$$\\end{document} planning algorithm. We employ linear operators applied to the GP kernel function to infer not only continuous position trajectories, but also velocities and accelerations. The use of linear functionals enable velocity and acceleration constraints given by the IMU measurements to be imposed on the position GP model. The results from both simulation and real-world experiments show that planning for IMU bias convergence helps minimize localization errors in state estimation frameworks.

An adaptive time-step energy-preserving variational integrator for flexible multibody system dynamics

An adaptive time-step variational integrator for simulating flexible multibody system dynamics is proposed. The integrator can adapt the time-step based on the variation of the system's energy. The flexible components in the system can undergo large overall motions and large deformations and are modelled by elements of absolute nodal coordinate formulations. In addition, a three-stage Newton-Raphson iteration method is developed to accurately solve the nonlinear discrete Euler-Lagrange equations in each time-step. Finally, three dynamic examples are presented to validate performance of the proposed integrator. Numerical results indicate that the proposed three-stage method has fast convergence rate. For the nonlinear flexible double pendulum system and the slider-crank mechanism, compared with constant time-step integrators, the proposed integrator can preserve the system's total energy more accurately and lead to more accurate dynamic responses. For the contact problem, the proposed integrator can quickly change the time-step size based on the sudden changes of energy to precisely compute the contact force and dynamic responses. Moreover, the proposed integrator can exactly preserve the displacement constraints and the velocity constraints simultaneously. In addition, it is noted that the computation efficiency of the proposed integrator needs to be further improved.

Quantitative Investigation of Parallel Interactions Between Charged Particles

On the premise that the charged particle is a normal geometry model, an expression of the migration current, displacement current and magnetic induction intensity generated by the charged particle motion is deduced according to the microscopic definition of current intensity, the total current law and the Biot-Savart law. Further calculate the electric field force between two charged particles in vacuum, give the velocity constraint relationship and velocity value criterion of the electric and magnetic field forces, and compare the consistency with the correlation results obtained considering the relativistic effect. It is pointed out that the magnetic field force is comparable to the electric field force only when the charged particle moves near the speed of light.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

Trajectory tracking of Jiaolong submersible with velocity constraints via dual closed-loop control

Trajectory tracking of Jiaolong submersible with velocity constraints via dual closed-loop control

Safety-critical anti-disturbance control of tugs for collaborative berthing

It is a challenging task for large ships themselves berthing in port areas even for an experienced captain. This paper addresses the collaborative berthing by utilizing tugs maneuvering at low speeds for operating a ship. A safety-critical anti-disturbance control method is proposed for collaborative berthing subject to the contact force constraint, velocity constraints, ship constraints referring to constraining the tugs velocities in the body frame of the ship and the angular rate of the ship, as well as ocean disturbances. First, a finite-time kinematic control law is developed for each tug to track the desired position and heading prescribed by using the relative distance between two tugs and the heading of port shoreline. Next, an extended state observer (ESO) based on robust exact differentiator (RED) is used for each tug to estimate the model uncertainties and environment disturbances. Then, a safety-critical anti-disturbance control law is designed for each tug by employing an RED-based ESO. Finally, through converting the contact force constraint and ship constraints to velocity constraints on tugs, a quadratic programming problem is solved to obtain the collaborative velocity signals for achieving the collaborative operation of the connected tugs subject to velocity constraints. It is proven that the closed-loop control system is finite-time input-to-state stable and the safety during collaborative berthing can be guaranteed in the presence of environmental disturbances. Simulation results are given to substantiate the efficacy of the proposed safety-critical anti-disturbance control method of tugs for collaborative berthing.